On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.
On the numerical modeling of deformations of pressurized martensitic thin films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
On the numerical solution of plate bending problems by hybrid methods
On the numerical treatment of the contact problem.
On the optimal design of elastic shafts
On the Signorini problem with friction in linear thermoelasticity: The quasi-coupled 2D-case
The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary of a polygonal domain is given. The rate of convergence is proved if the exact solution is sufficiently regular.
On the solution of a finite element approximation of a linear obstacle plate problem
In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably...
On the solution of a plate with ribs
On the solution of boundary value problems for sandwich plates
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
On the solution of one problem of the plate with ribs
In the present paper the convergence of the finite element method to the solution of the problem of a plate with ribs which are stiff against torsion in the sense of Vlasov is studied. According to the conclusions of a paper by the author and J. Haslinger it suffices to prove a density theorem (Theorem 2.1).
On the two-step iterative method of solving frictional contact problems in elasticity
A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation
The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the discrete problem...
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...
Operator-splitting schemes for solving elasticity problems.
Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints
We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
Optimal discretization of PML for elasticity problems.
Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Finite element semidiscrete approximations on nonlinear dynamic shallow shell models in considered. It is shown that the algorithm leads to global, optimal rates of convergence. The result presented in the paper improves upon the existing literature where the rates of convergence were derived for small initial data only [19].
Optimal L...-Error Estimates for Nonconforming and Mixed Finite Element Methods of Lowest Order.